I've lived in Logan Square for the previous 4 years and can tell you it is rapidly gentrifying. This is great for my home value, but not so much for some people who live here :(
That being said, there are good areas and bad areas in LS. The Milwaukee Corridor by the Congress Theater is getting a lot of love with 3 big TOD high rises that just went up and 1 that is almost finished right off of Milwaukee and Armitage. The home values are absolutely going up as is the rent. Most of the new TOD high rises are luxury condos and the one closest to me is trying to sell the condos for ~500-550k per. I'd say you're 3-5 years late in buying in the "down" market, but I do see things quickly getting nicer. The new owner of the Congress is working on getting it designated as a national historic landmark. When he does, the state will pay 25% of his rennovation fees and from the architectural drawings, it is going to be stunning. I see that helping property values quite a bit in a year or two when it is finished.
Keep in mind however, with literally 4 high rises built within the past 4 months, and a few more north towards the square and Logan Blvd, that the rental market is going to be saturated. That being said, this is an absolutely fantastic neighborhood and if you're able to get some property, now is the time! I just walked into an open house today for a 2 flat with a total income of $2700 for an asking price of $577k when I can get a 2 flat on the south side of chicago for around $180k or less with $2250-2500 depending on the location. Unless you buy a deal, this is a pricey hood.